On page optimization is the stuff that you tweak on your own website for the benefit of SEO. Such things include properly using H1 tags, having clean and well-optimized html code, keyword density, etc.

Off page optimization is the stuff that is not on your own website, and therefore you don't have direct control over, which affects your website's search engine rankings. Such things include the number of backlinks you have on other sites, word of mouth, whether you have articles from your site syndicated in the blogosphere, RSS feeds, etc.

In short you have to optimize your On page well to get a good Off page results...

These are also part of online marketing.

I think they both are Best and Important.
You should give priorities to both.

A.

So which one is important? Off the page or on the page.

Also Does SEO has got anything to do with Traffic?
I m still learning

Neither one is more important than another. Off page SEO is what gets the search engines coming to your site. On page SEO is what gets the search engines correctly crawling and indexing your site, and plays a key role in what keywords you rank for and how much content the engines think you have. (And content is key)

SEO is the tehnique of ranking well in the search engines. If you rank well, you get free traffic from them.

On page optimization involves improving website's contnets so that it may have high keyword density and power to attract visitors and effectve contents can retain some customers. However
off page optimization brings traffic for website from search engines and other websites. Read more about off page optimization.

they are both important...

On-Page SEO simply refers to the text and content on your web site pages. Basically editing your page and content so the Search Engine can find your webpage when a surfer is searching for your web sites particular topic.

Off-Page SEO in this we work out site of our web page. And not any need to use our web page that time. For Ex. Directory submission, Link Exchanges with relevant websites, Signature Link in forums, Article Marketing Etc...